Multiple-model based adaptive control design for parametric and matching uncertainties

This paper develops a new multiple-model adaptive control scheme to expand the capacity of state feedback state tracking adaptive control to handle both the plant-model matching and parameter uncertainties for single-input LTI systems. First, a multiple-model adaptive control design is derived for systems with uncertain parameter matrices in general forms, whose multiple controllers are implemented with multiple estimates of a single parameter vector defined under a matching condition for a single reference model system. Then, the new scheme is developed to relax the matching condition, using multiple reference model systems (only one of which is required to be able to match the controlled plant), and multiple controllers (which are updated from adaptive laws generated from multiple reference model systems based estimation errors), as two key features of the new design to deal with the matching uncertainty. A switching mechanism is constructed using those multiple estimation errors, capable of selecting the suitable control input from the multiple control signals (it is uncertain which of them can lead to a stable closed-loop system), to achieve the desired system performance. Such a new design has the capacity to relax some practical design conditions, as demonstrated by an aircraft flight control example.